Savings interest of a deceased person

Someone for whom I am executor died in December 2023. In February, HMRC sent me a simple tax calculation for them for 23-24, which showed they had overpaid income tax, and I received a cheque for the overpayment. However, I notice that in the calculation, the figure used for untaxed bank interest was simply a repeat of the figure from 22-23, not based on actual interest earned in 23-24 (to date of death). Now that the tax year is over, banks will be supplying actual interest numbers to HMRC. If the deceased earned more interest in 23-24 than the previous year, and owes tax on it, will HMRC contact me, or is it up to me work this out? Or is it case closed after the simple tax calculation? NB the interest I am talking about is that received by the deceased when alive, not estate interest.

Hi Elvira,
While it is unlikely that any update to the interest figure would cause a change to the overall calculation, if any additional tax is due, we would contact you to discuss this.
Thank you.